3.17 Quick-Revision Formula Sheet

Use this box for a final glance the night before your exam — every formula from this chapter in one place.

• Percentage = (Part ÷ Base) × 100
• % Increase = [(New − Original) ÷ Original] × 100
• % Decrease = [(Original − New) ÷ Original] × 100
• Value after r% increase = Original × (1 + r/100); after r% decrease = Original × (1 − r/100)
• Successive % change: Net% = a + b + ab/100 (a, b positive for increase, negative for decrease)
• Same % up then down: Net change = −a²/100 (always a net decrease)
• Constant expenditure, price up r%: reduce consumption by r/(100+r) × 100
• Constant expenditure, price down r%: increase consumption by r/(100−r) × 100
• Population/value after n years of growth: P(1 + r/100)ⁿ; of decline or depreciation: P(1 − r/100)ⁿ
• % Error = (|Measured − True|) ÷ True × 100
• Pass marks = Pass% × Maximum marks; (difference in %) × Maximum marks/100 = difference in actual marks
• Valid votes = Total voters × (1 − Invalid%/100); each candidate’s votes = their % share × Valid votes
• Ratio a : b → % share of a = a/(a+b) × 100; % share of b = b/(a+b) × 100
• Reverse percentage: Original = Final value ÷ (1 ± r/100)